Interval

You are given $n$ intervals, the $j$-th of which is $I_j = [l_j, r_j]$.

The beauty of $[L, R]$ is the length covered by $\bigcup_{i = L}^{R} [l_i, r_i]$.

You are given $m$ queries. The $i$-th query is $[A_i, B_i]$, and you need to answer the following.

Choose $[L_i, R_i]$ uniformly at random from all integer pairs with $A_i \le L_i \le R_i \le B_i$. Find the expected beauty of $[L_i, R_i]$.

The expected value can be written as a fraction $p/q$ with coprime non-negative integers $p$ and $q$. Print $p \cdot q^{-1} \bmod 998\,244\,353$.

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 2 \cdot 10^5$).

Each of the next $n$ lines contains $l_j$ and $r_j$ ($0 \le l_j < r_j \le 10^8$).

Each of the next $m$ lines contains $A_i$ and $B_i$ ($1 \le A_i \le B_i \le n$).

Print $m$ lines. Line $i$ contains the answer for the $i$-th query, taken modulo $998\,244\,353$.

The input and output are large, so use fast I/O to avoid exceeding the time limit.